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Magnetically Induced Rotating Rayleigh-Taylor Instability

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Instabilities of variable-density swirling flows.

Bastien Di Pierro¹, Malek Abid

¹IRPHE-UMR 6594, Technopôle de Château-Gombert, 49 rue Joliot Curie, BP 146, 13384 Marseille Cedex 13, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|January 15, 2011

Summary

This summary is machine-generated.

This study addresses limitations in modeling inviscid swirling flows, developing a new asymptotic analysis for variable velocity profiles. The findings offer improved analytical methods for understanding fluid dynamics in complex flow scenarios.

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Area of Science:

Fluid Dynamics
Asymptotic Analysis
Hydrodynamics

Background:

Inviscid swirling flows are often modeled using axisymmetric velocity profiles.
Existing asymptotic analysis methods (Leibovich and Stewartson) have limitations when velocity gradients satisfy specific conditions.

Purpose of the Study:

To develop an analytical method for modeling inviscid swirling flows where standard asymptotic procedures fail.
To investigate the behavior of these flows under weak variations in axial and azimuthal velocities.

Main Methods:

Applied asymptotic analysis for large axial (k) and azimuthal (m) wave numbers.
Investigated cases where the Leibovich and Stewartson condition kW'(r) + mΩ'(r) = 0 is not met for all r.
Validated analytical results with numerical computations of linearized Euler equations for variable-density Batchelor-like vortices.

Main Results:

Developed a successful asymptotic analysis for inviscid swirling flows with varying velocity profiles, overcoming limitations of previous methods.
Demonstrated good agreement between analytical predictions and numerical results, even for low wave numbers (m and k).

Conclusions:

The proposed asymptotic analysis provides a robust method for studying complex swirling flows.
The findings are applicable to a range of fluid dynamics problems involving vortex dynamics and stability.